Out of all the skills, which ones benefit with extra IP and which don't?

I was wondering which IP skills can be raised higher than the minimum required to equip a weapon or cast a nano and add performance to the player’s character, and which should just be set exactly to what is needed to equip a weapon and cast a nano.

So like Mat Met or Bio met; just the minimum for the max nano or does even higher than the minimum yield benefits?

most of the time, just hitting the base requirements for a nano is all that is needed. Some professions like NTs benefit from keeping MC maxed, because it makes some damage nanos do more damage the higher MC you have. Other examples is something like, Uncontrollable Body Tremors for doc, while you can cast the nanos with base skills, you might get resisted a lot on SL mobs, so you might want to raise those skills past minimum. Self buffs, usually minimum works fine.

For weapons it depends on the weapon stats.
Let’s have a look at the Envy of the Xan Envy of the Xan - Anarchy Online Items Database
U need just 1689 Fullauto to equip it but ur FA recharge will be way to high with just that.
U don’t want a Fullauto just every minute or so. To maximize the Damage u need 2420 Fullauto skill to get it down to one FA every 11.2s.
Burst is a total different thing with that Weapon, u need 1689 Burst skill for eqipping but every Point over 675 is wasted once u have it equipped.
As for the SMG skill for that weapon u just have to check that u reach an attack rating from 2750. Attack rating comes from SMG skill + add all off. Everything over 2750 will not increase the damage any further. An exception is PvP where even more attackrating will make enemys dodge less of ur attacks.